hai1 wrote:
Ans:
C
My reasoning: Slope= -b/a
1. Slope is negative
For slope to be negative, b & a> 0; or b & a<0;
Hence it is not possible to tell if b is postive.
2. a<b
We cannot tell anything about this.
1 & 2 combined: Even this will not give us any information about b.
If a<b and a&b>0; -b/a will be -ve; Is b > 0? yes
If a<b and a&b<0; -b/a will be -ve; Is b < 0? No
So how is this answer right?
I think you are forgetting to include key info from the question stem: the line passes through origin.
You have to combine the info from (1) with the info in the question stem. (1) tells us the slope is negative. So, (reading from left to right) the line "falls". But if it is passing through the origin, this means the line is falling from the second quadrant (upper-left) into the fourth quadrant (lower-right). In the second quadrant, y values are positive while x values are negative; in the fourth quadrant, it is the other way around. So from (1), we know that one coordinate in (a,b) is negative while the other positive; as Rohan put it, a and b have different signs. Combining this with (2), clearly a is negative and b is positive.
____________
Takeaways: -evaluate each statement independently from each other BUT IN CONJUNCTION WITH THE QUESTION STEM!
- many coordinate geometry problems are better approached qualitatively (rather than algebraically), either visualizing or drawing out a quick coordinate plane on your scratchpaper.
